NCERT Solutions For Class 11 Maths Chapter 2: Relations and Functions

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NCERT Solutions for class 11 mathematics Chapter 2 Relations and Functions are provided in the article below. Relations and functions define a mapping between two sets (Inputs and Outputs) such that they have ordered pairs of the form (Input, Output). Class 11 Mathematics Chapter covers important concepts including Addition of Two Real Functions, Real Valued Functions, and Ordered Pairs.

Download: NCERT Solutions for Class 11 Mathematics Chapter 2 pdf

Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions are as provided below:

Also check: Relations and Functions

Important Topics for Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

Important Topics for Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions are as follows:

Cartesian Product of Sets

Cartesian product is the product of any two sets. This product’s resultant set contains all possible and ordered pairs so that the first element of the pair belongs to the first set and the second element belongs to the second set.

Example. Given two sets C = {1,2,6} and D = {8,3}. Find the cartesian product C × D.

Solution: The first element 1 is taken from the set C {1,2,6} and the second element 8 is taken from the second set D {8, 3} to form the first ordered pair (1,8).

Same step is repeated until all possible combinations are chosen. After multiplying two sets C and D, 6 ordered pairs are obtained: {(1,8),(1,3),(2,8),(2,3),(6,8),(6,3)}.

This is the cartesian product of the two sets C and D.

Relations

Relations are used to describe a connection between elements of two sets. They help to map elements of one set (domain) to elements of another set (range). The resulting ordered pairs are of the form (input, output). It can also be said that a function is a subset of a relation.

Example: Find the inverse relation of R = {(4, 8), (-3, -6), (7.1, 2.3)}

Solution: Inverse relation is defined as R-1 = {(y, x) : (x, y) ∈ R}

Therefore, R-1 = {(8, 4), (-6, -3), (2.3, 7.1)}

Therefore, the inverse relation R-1 = {(8, 4), (-6, -3), (2.3, 7.1)}

Functions

Function is the relation between a set of inputs and a set of permissible outputs. Each input is related to exactly one output.

Example: In the function f(x)=x² f (x) = x² any input for x will give one output only.

NCERT Solutions For Class 11 Maths Chapter 2 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 2 Relations and Functions under different exercises are as follows:

Also check:

Chapter Related Topics
Polynomial Function	Greatest Integer Function	Function notation formula
Product to sum formula	Analytic Function	Ordered Pairs

Also check:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Arithmetic

CBSE CLASS XII Related Questions

1.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.
2.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :
3.
An NGO organises a charity event in which they decide to distribute woollen caps to protect children from winter. The caps to be distributed are in three separate boxes, Box I has 30 red caps, Box II has 20 red and 10 green caps, and Box III has 30 green caps. The probability that a Box i is selected and a cap picked out is i/6, where i = 1, 2, 3.
Based on the above information, answer the following questions :
4.
Evaluate:
\[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]
View Solution
5.
Find a point on the line \( \frac{x - 2}{3} = \frac{1 - y}{2} = \frac{z - 3}{2} \) at a distance of \( \sqrt{2} \) units from the point \( (1, 2, 3) \).
View Solution
6.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]
View Solution

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NCERT Solutions For Class 11 Maths Chapter 2: Relations and Functions

Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

Important Topics for Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

NCERT Solutions For Class 11 Maths Chapter 2 Exercises:

CBSE CLASS XII Related Questions

1.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

2.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :

4.
Evaluate:
\[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]

5.
Find a point on the line \( \frac{x - 2}{3} = \frac{1 - y}{2} = \frac{z - 3}{2} \) at a distance of \( \sqrt{2} \) units from the point \( (1, 2, 3) \).

6.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

Similar Mathematics Concepts

Comments

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NCERT Solutions For Class 11 Maths Chapter 2: Relations and Functions

Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

Important Topics for Class 11 Maths NCERT Solutions Chapter 2 Relations and Functions

NCERT Solutions For Class 11 Maths Chapter 2 Exercises:

CBSE CLASS XII Related Questions

1.A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

2.At a birthday party, children are being served orange juice in conical cups, as shown in the figure. Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.On the basis of the above information, answer the following questions :

4.Evaluate:\[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]

5.Find a point on the line \( \frac{x - 2}{3} = \frac{1 - y}{2} = \frac{z - 3}{2} \) at a distance of \( \sqrt{2} \) units from the point \( (1, 2, 3) \).

6. Find: The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
A carpenter needs to design a wooden box in the shape of a cuboid such that the sum of its length and breadth is 3 cm more than its height. Twice of its length, thrice of its breadth and its height add up to 10 cm. Its breadth added to 7 times its height is 1 cm less than 3 times its length.

2.
At a birthday party, children are being served orange juice in conical cups, as shown in the figure.

Each cup is 15 cm deep and has a radius 5 cm. The juice is being poured into this cup at a rate of 0·1 cm3/s.
On the basis of the above information, answer the following questions :

4.
Evaluate:
\[ \int_{0}^{1} \frac{x \tan^{-1}x}{(1+x^2)^{3/2}}\,dx \]

5.
Find a point on the line \( \frac{x - 2}{3} = \frac{1 - y}{2} = \frac{z - 3}{2} \) at a distance of \( \sqrt{2} \) units from the point \( (1, 2, 3) \).

6.
Find:

The shortest distance between the lines: \[ \vec{r}=(4+\lambda)\hat{i}+(2\lambda-1)\hat{j}-3\lambda\hat{k} \] and \[ \vec{r}=(1+2\mu)\hat{i}+(4\mu-1)\hat{j}+(2-5\mu)\hat{k} \]